C₂×#2352 #34115

order	256
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	Aut(G) order 1048576
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

1947 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 5 generators on 18 points:

(1,2);(3,4)(5,6)(7,8,9,10)(12,13)(16,17);(4,6)(11,12,15,13)(14,17,18,16);(11,13,15,12)(14,17,18,16);(3,4)(5,6)(11,14)(12,16)(13,17)(15,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27103);